Recognition of mathematical formulas based on support vector machines
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摘要: 数学公式识别在拍照搜题、自动阅卷和题库建设等智慧教育任务中有着广泛的应用.由于这些应用中数学公式大多以图片的形式存在，因此识别图片中的数学公式成为智慧教育领域的重要研究问题之一.数学公式结构复杂，从图片中识别数学公式远比一般的光学符号识别要复杂得多.将公式识别分为字符分割、符号识别和公式重组这3个步骤：首先，综合运用投影和连通域方法将字符从图片中分割出来；其次，基于单个字符的区域像素数占总像素比例提取字符特征，建立监督学习模型识别字符；最后，利用每个字符在公式中出现的位置对数学公式进行重组.真实数据集上的实验结果表明，本文提出的数学公式识别方法准确率高达98.0%.Abstract: The recognition of mathematical formulas has been widely used in intelligent education applications, such as searching for answers to questions in image format, automatic marking, and constructing a database of questions. Mathematical formulas often exist in the form of images in many applications; hence, identifying the formulas in these images is an important research topic in the field of intelligent education. Given the complex structure of mathematical formulas, however, recognizing their presence within images is far more complicated than a general optical character recognition task. This paper decomposes formula recognition into three steps:character segmentation, character recognition, and formula reconstruction. First, the characters are separated from an image by using a combination of projection and connected-domain methods. Second, the features of characters are extracted based on the proportion of pixels in a single character relative to pixels in all characters, and a supervised learning model is established to identify each character. Finally, the mathematical formula is reconstructed based on the location of each character in the formula. Experimental results on a real data set show the proposed mathematical formula recognition method can achieve an accuracy of up to 98.0%.
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表 1 SVM模型默认参数
Tab. 1 Default parameters of the SVM model
参数 值 说明 $C$ 1.0 误差项的惩罚参数 kernel rbf 高斯核函数 cache_size 200 核函数cache缓存大小 class_weight None 分类权重, None表示权重相同 max_iter -1 最大迭代次数, -1表示无穷迭代 decision_function_shape OVO 一对一方法, 用于解决多分类问题 
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表 2 分类器运用不同特征的识别效果比较
Tab. 2 A comparison of recognition effects of different features in the SVM classifier
评估标准 识别率/% 查准率/% 查全率/% $F$1-score/% 原特征 97.1 97.6 97.3 97.1 改进特征 98.0 98.3 98.1 98.0
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表 3 不同分类器使用优化特征的识别效果比较
Tab. 3 A comparison of recognition effects of different classifiers using optimized features
分类器 评估标准 识别率/% 查准率/% 查全率/% $F$1-score/% 决策树 97.0 97.2 96.9 97.0 MLP神经网络 96.6 96.6 96.5 96.1 OVO SVMs 98.0 98.3 98.1 98.0
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